We have a singer who practically insists on doing Mustang Sally and Crossroads at every gig. I've complained some, but of course I play the songs when they come up, since standing there with crossed arms and a frown isn't an option. These are not the only "classics" we do, but they are the ones that I dislike more than the others.

We have plenty of songs in the repertoire so its not like we need to do them all the time.

What to do, what to do... If I had my druthers, we'd put these songs in the vault, only to come out when requested.

Audience first, no doubt. There's a story in an Aerosmith book that I read, where is talks about how they grew weary of playing Dream On after doing it so many times. Yet, they knew it was something the crowd came and expected to hear. That's just the way it goes for some of those timeless tunes...we musicians have to bite the bullet to play what works.

I can not tell you how many times I've heard people say; "how many more versions of (insert song name) must we hear," or "is that the only song anybody does by (insert band name)."

So we have a short list of tunes that are only played by request and encourage said patron to buy the band a round. We then play that up to get the patrons to buy another round for themselves and have a toast (for whatever reason) with the band. Makes us look good at the cash register and bar management likes sales.

I'm going to say something super unpopular here, so I'll hedge it with "No disrespect" or "I'm just saying..."

Every outdoor event with a band I've been to since I was old enough to start paying attention, has played the same set of songs from the 60's and 70's, over and over and over again. So some of those songs were old 25 years ago, and have only gotten older, as have the audience, and yet they keep playing them.
What's my point? Is Mustang Sally really that tired in the context of the rest of your set? Is there one song in that set written between 1990 and 2010? If not, aren't they all a little tired?

If your audience is still responding to said "tired old songs" then the problem is yours, however there are things you can do to spice them up and make them more interesting in much the same way you might try a new move in the boudoir to spice things up a bit if you catch my drift.

change the arrangement
add an audience sing along part if thats appropriate
do a medley of a couple of those kinds of tunes
change the words to more provactive lyrics ( yeah, go all sexy and stuff)
try and make them fun again